{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "google",
   "metadata": {},
   "source": [
    "##### Copyright 2025 Google LLC."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "apache",
   "metadata": {},
   "source": [
    "Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "you may not use this file except in compliance with the License.\n",
    "You may obtain a copy of the License at\n",
    "\n",
    "    http://www.apache.org/licenses/LICENSE-2.0\n",
    "\n",
    "Unless required by applicable law or agreed to in writing, software\n",
    "distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "See the License for the specific language governing permissions and\n",
    "limitations under the License.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "basename",
   "metadata": {},
   "source": [
    "# set_covering3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "link",
   "metadata": {},
   "source": [
    "<table align=\"left\">\n",
    "<td>\n",
    "<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/contrib/set_covering3.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
    "</td>\n",
    "<td>\n",
    "<a href=\"https://github.com/google/or-tools/blob/main/examples/contrib/set_covering3.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
    "</td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "doc",
   "metadata": {},
   "source": [
    "First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "install",
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install ortools"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "description",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "  Set covering in Google CP Solver.\n",
    "\n",
    "  Problem from\n",
    "  Katta G. Murty: 'Optimization Models for Decision Making', page 302f\n",
    "  http://ioe.engin.umich.edu/people/fac/books/murty/opti_model/junior-7.pdf\n",
    "\n",
    "  10 senators making a committee, where there must at least be one\n",
    "  representative from each group:\n",
    "  group:        senators:\n",
    "  southern      1 2 3 4 5\n",
    "  northern      6 7 8 9 10\n",
    "  liberals      2 3 8 9 10\n",
    "  conservative  1 5 6 7\n",
    "  democrats     3 4 5 6 7 9\n",
    "  republicans   1 2 8 10\n",
    "\n",
    "  The objective is to minimize the number of senators.\n",
    "\n",
    "  Compare with the following models:\n",
    "  * MiniZinc: http://www.hakank.org/minizinc/set_covering3_model.mzn (model)\n",
    "              http://www.hakank.org/minizinc/set_covering3.mzn (data)\n",
    "  * Comet   : http://www.hakank.org/comet/set_covering3.co\n",
    "  * ECLiPSe : http://www.hakank.org/eclipse/set_covering3.ecl\n",
    "  * SICStus : http://hakank.org/sicstus/set_covering3.pl\n",
    "  * Gecode  : http://hakank.org/gecode/set_covering3.cpp\n",
    "\n",
    "\n",
    "  This model was created by Hakan Kjellerstrand (hakank@gmail.com)\n",
    "  Also see my other Google CP Solver models:\n",
    "  http://www.hakank.org/google_or_tools/\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "code",
   "metadata": {},
   "outputs": [],
   "source": [
    "from ortools.constraint_solver import pywrapcp\n",
    "\n",
    "\n",
    "def main(unused_argv):\n",
    "\n",
    "  # Create the solver.\n",
    "  solver = pywrapcp.Solver(\"Set covering\")\n",
    "\n",
    "  #\n",
    "  # data\n",
    "  #\n",
    "  num_groups = 6\n",
    "  num_senators = 10\n",
    "\n",
    "  # which group does a senator belong to?\n",
    "  belongs = [\n",
    "      [1, 1, 1, 1, 1, 0, 0, 0, 0, 0],  # 1 southern\n",
    "      [0, 0, 0, 0, 0, 1, 1, 1, 1, 1],  # 2 northern\n",
    "      [0, 1, 1, 0, 0, 0, 0, 1, 1, 1],  # 3 liberals\n",
    "      [1, 0, 0, 0, 1, 1, 1, 0, 0, 0],  # 4 conservative\n",
    "      [0, 0, 1, 1, 1, 1, 1, 0, 1, 0],  # 5 democrats\n",
    "      [1, 1, 0, 0, 0, 0, 0, 1, 0, 1]  # 6 republicans\n",
    "  ]\n",
    "\n",
    "  #\n",
    "  # declare variables\n",
    "  #\n",
    "  x = [solver.IntVar(0, 1, \"x[%i]\" % i) for i in range(num_senators)]\n",
    "\n",
    "  #\n",
    "  # constraints\n",
    "  #\n",
    "\n",
    "  # number of assigned senators (to minimize)\n",
    "  z = solver.Sum(x)\n",
    "\n",
    "  # ensure that each group is covered by at least\n",
    "  # one senator\n",
    "  for i in range(num_groups):\n",
    "    solver.Add(\n",
    "        solver.SumGreaterOrEqual(\n",
    "            [x[j] * belongs[i][j] for j in range(num_senators)], 1))\n",
    "\n",
    "  objective = solver.Minimize(z, 1)\n",
    "\n",
    "  #\n",
    "  # solution and search\n",
    "  #\n",
    "  solution = solver.Assignment()\n",
    "  solution.Add(x)\n",
    "  solution.AddObjective(z)\n",
    "\n",
    "  collector = solver.LastSolutionCollector(solution)\n",
    "  solver.Solve(\n",
    "      solver.Phase(x, solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT),\n",
    "      [collector, objective])\n",
    "\n",
    "  print(\"z:\", collector.ObjectiveValue(0))\n",
    "  print(\"x:\", [collector.Value(0, x[i]) for i in range(num_senators)])\n",
    "  for j in range(num_senators):\n",
    "    if collector.Value(0, x[j]) == 1:\n",
    "      print(\"Senator\", j + 1, \"belongs to these groups:\", end=\" \")\n",
    "      for i in range(num_groups):\n",
    "        if belongs[i][j] == 1:\n",
    "          print(i + 1, end=\" \")\n",
    "      print()\n",
    "\n",
    "  print()\n",
    "  print(\"failures:\", solver.Failures())\n",
    "  print(\"branches:\", solver.Branches())\n",
    "  print(\"WallTime:\", solver.WallTime())\n",
    "\n",
    "\n",
    "main(\"cp sample\")\n",
    "\n"
   ]
  }
 ],
 "metadata": {
  "language_info": {
   "name": "python"
  }
 },
 "nbformat": 4,
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